Nodal
domains of graphs
Türker Biyikoglu
Department for Applied
Statistics and Data Processing, University of Economics and Business Administration,
Augasse 2-6, A-1090 Vienna, Austria
Let
f be a
real function on the vertices of a graph G = 3D(V, E). A strong (weak) nodal
domain of f is a maximal connected induced subgraph G[W] of G with vertex
set W
such that f(x)f(y) > 0
(f(x)f(y) ≥ 0)
for all x, y
Î
W. I
will talk about the number of strong and weak nodal domains of some graph
classes, where the function f is an eigenvector of Laplace matrix (Schrödinger
operator) of a graph. These eigenvectors are of interest in simplified
quantum mechanical models of organic molecules.
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